CS381-2006fa-prelim1 - CS 381 Fall 2006 First Mid Term...

CS 381 First Mid Term Friday, Oct. 27, 2006 Fall 2006 Upson B17 This is a 50-minute in class closed book exam. All questions are straightforward and you should have no trouble doing them. Please show all work and write legibly. Grading will take into account the clarity of your answer. 1. Write a regular expression denoting all strings of 0’s and 1’s in which if there are two adjacent 0’s in the string, then there will also be two adjacent 1’s somewhere in the string. Give a brief English explanation as to how your regular expression works. 2. State the pumping lemma for regular sets. Prove that the set {}|0ija bij>>is not regular using the pumping lemma for regular sets. 3. Let ()0,,,,MQqFδ=Σbe a finite automaton and let ()00,,,,,,PQqZFδ=Σ Γbe a pushdown automaton that accepts by final state.

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